
# Let’s create a dataset to work with and plot a histogram to visualise
import numpy as np
from scipy import stats

import matplotlib
import matplotlib.pyplot as plt
%matplotlib inline
matplotlib.style.use('ggplot')

np.random.seed(1)
data = np.round(np.random.normal(5, 2, 100))
plt.hist(data, bins=10, range=(0,10), edgecolor='black')
plt.show()


# Measures of Central Tendency

# Calculating the mean
mean = np.mean(data)
mean

5.1


# Measures of Central Tendency

# Calculating the median
np.median(data)

5.0


# Measures of Central Tendency

# Calculating the mode
mode = stats.mode(data)

print("The modal value is {} with a count of {}".format(mode.mode[0], mode.count[0]))

The modal value is 5.0 with a count of 23


# The range gives a measure of how spread apart the values are.

# Calculating the Range
np.ptp(data)

9.0


# Variance is a measure of how variable the data is

# Calculating the Variance
np.var(data)

3.07


# The variance can get very large for large data sets and so we will often use the standard deviation,
# which is the square root of the variance

# Calculating the Standard Deviation
np.std(data)

1.752141546793523


# The standard error of the mean (SE of the mean) estimates the variability
#between sample means that you would obtain if you took multiple samples from the same population.
# The standard error of the mean estimates the variability between samples
# whereas the standard deviation measures the variability within a single sample.

# Calculating the Standard Error
stats.sem(data)

0.1760968512214259


import seaborn as sns
sns.set(style="darkgrid")

# Load an example dataset with long-form data
fmri = sns.load_dataset("fmri")

# Plot the responses for different events and regions
sns.lineplot(x="timepoint", y="signal",
             hue="region", style="event",
             data=fmri)

<AxesSubplot:xlabel='timepoint', ylabel='signal'>


import pandas as pd
df = pd.DataFrame(dict(time=pd.date_range("2017-1-1", periods=500),
                       value=np.random.randn(500).cumsum()))
g = sns.relplot(x="time", y="value", kind="line", data=df)
g.fig.autofmt_xdate()


import seaborn as sns
sns.set(style="ticks")

df = sns.load_dataset('iris')
sns.pairplot(df, hue="species")

<seaborn.axisgrid.PairGrid at 0x7fc8e8a60610>


import seaborn as sns
import matplotlib.pyplot as plt
sns.set(style="whitegrid")

# Load the example diamonds dataset
diamonds = sns.load_dataset("diamonds")

# Draw a scatter plot while assigning point colors and sizes to different
# variables in the dataset
f, ax = plt.subplots(figsize=(6.5, 6.5))
sns.despine(f, left=True, bottom=True)
clarity_ranking = ["I1", "SI2", "SI1", "VS2", "VS1", "VVS2", "VVS1", "IF"]
sns.scatterplot(x="carat", y="price",
                hue="clarity", size="depth",
                palette="ch:r=-.2,d=.3_r",
                hue_order=clarity_ranking,
                sizes=(1, 8), linewidth=0,
                data=diamonds, ax=ax)

<AxesSubplot:xlabel='carat', ylabel='price'>


import seaborn as sns
import matplotlib.pyplot as plt

sns.set(style="ticks")

# Initialize the figure with a logarithmic x axis
f, ax = plt.subplots(figsize=(7, 6))
ax.set_xscale("log")

# Load the example planets dataset
planets = sns.load_dataset('planets')

# Plot the orbital period with horizontal boxes
sns.boxplot(x="distance", y="method", data=planets,
            whis=[0, 100], palette="vlag")

# Add in points to show each observation
sns.swarmplot(x="distance", y="method", data=planets,
              size=2, color=".3", linewidth=0)

# Tweak the visual presentation
ax.xaxis.grid(True)
ax.set(ylabel="")
sns.despine(trim=True, left=True)

/Users/arminhadzalic/opt/anaconda3/envs/dataexploration/lib/python3.8/site-packages/seaborn/categorical.py:1296: UserWarning: 16.5% of the points cannot be placed; you may want to decrease the size of the markers or use stripplot.
  warnings.warn(msg, UserWarning)


import seaborn as sns
sns.set(style="darkgrid")

tips = sns.load_dataset('tips')
g = sns.jointplot("total_bill", "tip", data=tips,
                  kind="reg", truncate=False,
                  xlim=(0, 60), ylim=(0, 12),
                  color="m", height=7)

/Users/arminhadzalic/opt/anaconda3/envs/dataexploration/lib/python3.8/site-packages/seaborn/_decorators.py:36: FutureWarning: Pass the following variables as keyword args: x, y. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.
  warnings.warn(


import numpy as np
import pandas as pd
import seaborn as sns
import matplotlib.pyplot as plt

sns.set(style="ticks")

# Create a dataset with many short random walks
rs = np.random.RandomState(4)
pos = rs.randint(-1, 2, (20, 5)).cumsum(axis=1)
pos -= pos[:, 0, np.newaxis]
step = np.tile(range(5), 20)
walk = np.repeat(range(20), 5)
df = pd.DataFrame(np.c_[pos.flat, step, walk],
                  columns=["position", "step", "walk"])

# Initialize a grid of plots with an Axes for each walk
grid = sns.FacetGrid(df, col="walk", hue="walk", palette="tab20c",
                     col_wrap=4, height=1.5)

# Draw a horizontal line to show the starting point
grid.map(plt.axhline, y=0, ls=":", c=".5")

# Draw a line plot to show the trajectory of each random walk
grid.map(plt.plot, "step", "position", marker="o")

# Adjust the tick positions and labels
grid.set(xticks=np.arange(5), yticks=[-3, 3],
         xlim=(-.5, 4.5), ylim=(-3.5, 3.5))

# Adjust the arrangement of the plots
grid.fig.tight_layout(w_pad=1)


# IF you receive an error after running this cell, open "Anaconda Prompt" and type: conda install plotly

# Basic Box Plot
import plotly.graph_objects as go
import numpy as np
np.random.seed(1)

y0 = np.random.randn(50) - 1
y1 = np.random.randn(50) + 1

fig = go.Figure()
fig.add_trace(go.Box(y=y0))
fig.add_trace(go.Box(y=y1))

fig.show()

# Grouped Box Plots
import plotly.graph_objects as go

x = ['day 1', 'day 1', 'day 1', 'day 1', 'day 1', 'day 1',
     'day 2', 'day 2', 'day 2', 'day 2', 'day 2', 'day 2']

fig = go.Figure()

fig.add_trace(go.Box(
    y=[0.2, 0.2, 0.6, 1.0, 0.5, 0.4, 0.2, 0.7, 0.9, 0.1, 0.5, 0.3],
    x=x,
    name='kale',
    marker_color='#3D9970'
))
fig.add_trace(go.Box(
    y=[0.6, 0.7, 0.3, 0.6, 0.0, 0.5, 0.7, 0.9, 0.5, 0.8, 0.7, 0.2],
    x=x,
    name='radishes',
    marker_color='#FF4136'
))
fig.add_trace(go.Box(
    y=[0.1, 0.3, 0.1, 0.9, 0.6, 0.6, 0.9, 1.0, 0.3, 0.6, 0.8, 0.5],
    x=x,
    name='carrots',
    marker_color='#FF851B'
))

fig.update_layout(
    yaxis_title='normalized moisture',
    boxmode='group'
# group together boxes of the different traces for each value of x
)
fig.show()


# Basic Histogram
import plotly.graph_objects as go

import numpy as np
np.random.seed(1)

x = np.random.randn(500)

fig = go.Figure(data=[go.Histogram(x=x)])
fig.show()

# Overlaid Histogram
import plotly.graph_objects as go

import numpy as np

x0 = np.random.randn(500)
# Add 1 to shift the mean of the Gaussian distribution
x1 = np.random.randn(500) + 1

fig = go.Figure()
fig.add_trace(go.Histogram(x=x0))
fig.add_trace(go.Histogram(x=x1))

# Overlay both histograms
fig.update_layout(barmode='overlay')
# Reduce opacity to see both histograms
fig.update_traces(opacity=0.75)
fig.show()


# Basic Distplot
import plotly.figure_factory as ff
import numpy as np
np.random.seed(1)

x = np.random.randn(1000)
hist_data = [x]
group_labels = ['distplot'] # name of the dataset

fig = ff.create_distplot(hist_data, group_labels)
fig.show()

# Plot Multiple Datasets
import plotly.figure_factory as ff
import numpy as np

# Add histogram data
x1 = np.random.randn(200) - 2
x2 = np.random.randn(200)
x3 = np.random.randn(200) + 2
x4 = np.random.randn(200) + 4

# Group data together
hist_data = [x1, x2, x3, x4]

group_labels = ['Group 1', 'Group 2', 'Group 3', 'Group 4']

# Create distplot with custom bin_size
fig = ff.create_distplot(hist_data, group_labels, bin_size=.2)
fig.show()


# Basic Density Heatmap
import plotly.express as px
df = px.data.tips() 

fig = px.density_heatmap(df, x="total_bill", y="tip")
fig.show()

# Multiple Density Heatmap
import plotly.express as px
df = px.data.tips()

fig = px.density_heatmap(df, x="total_bill", y="tip", facet_row="sex", facet_col="smoker")
fig.show()


# Basic Violin Plot
import plotly.express as px

df = px.data.tips()
fig = px.violin(df, y="total_bill")
fig.show()

# Multiple Violin Plot
import plotly.express as px

df = px.data.tips()
fig = px.violin(df, y="tip", x="smoker", color="sex", box=True, points="all",
          hover_data=df.columns)
fig.show()


# Linear Trendlines
import plotly.express as px

df = px.data.tips()
fig = px.scatter(df, x="total_bill", y="tip", trendline="ols")
fig.show()

# Non-Linear Trendlines
import plotly.express as px

df = px.data.gapminder().query("year == 2007")
fig = px.scatter(df, x="gdpPercap", y="lifeExp", color="continent", trendline="lowess")
fig.show()


df.head(5)


df.lifeExp.max()

82.603


# Basic Scatterplot Matrix
import plotly.express as px
df = px.data.iris()
fig = px.scatter_matrix(df)
fig.show()

# Styled Scatterplot Matrix
import plotly.express as px
df = px.data.iris()
fig = px.scatter_matrix(df,
    dimensions=["sepal_width", "sepal_length", "petal_width", "petal_length"],
    color="species", symbol="species",
    title="Scatter matrix of iris data set",
    labels={col:col.replace('_', ' ') for col in df.columns}) # remove underscore
fig.update_traces(diagonal_visible=False)
fig.show()


import matplotlib.pyplot as plt
import numpy as np

# Random test data
np.random.seed(123)
all_data = [np.random.normal(0, std, 100) for std in range(1, 4)]

fig, axes = plt.subplots(nrows=1, ncols=2, figsize=(9, 4))

# rectangular box plot
bplot1 = axes[0].boxplot(all_data,
                         vert=True,   # vertical box aligmnent
                         patch_artist=True)   # fill with color

# notch shape box plot
bplot2 = axes[1].boxplot(all_data,
                         notch=True,  # notch shape
                         vert=True,   # vertical box aligmnent
                         patch_artist=True)   # fill with color

# fill with colors
colors = ['pink', 'lightblue', 'lightgreen']
for bplot in (bplot1, bplot2):
    for patch, color in zip(bplot['boxes'], colors):
        patch.set_facecolor(color)

# adding horizontal grid lines
for ax in axes:
    ax.yaxis.grid(True)
    ax.set_xticks([y+1 for y in range(len(all_data))], )
    ax.set_xlabel('xlabel')
    ax.set_ylabel('ylabel')

# add x-tick labels
plt.setp(axes, xticks=[y+1 for y in range(len(all_data))], xticklabels=['x1', 'x2', 'x3'])

plt.show()


import numpy as np
import matplotlib.pyplot as plt

# example data
x = np.arange(0.1, 4, 0.5)
y = np.exp(-x)

fig, ax = plt.subplots()
ax.errorbar(x, y, xerr=0.2, yerr=0.4)
plt.show()


import numpy as np
import matplotlib.pyplot as plt
from matplotlib import mlab

np.random.seed(0)

mu = 200
sigma = 25
n_bins = 50
x = np.random.normal(mu, sigma, size=100)

fig, ax = plt.subplots(figsize=(8, 4))

# plot the cumulative histogram
n, bins, patches = ax.hist(x, n_bins, histtype='step',
                           cumulative=True, label='Empirical')

# Add a line showing the expected distribution.
from scipy.stats import norm
y = norm.pdf(bins, mu, sigma).cumsum()
y /= y[-1]

ax.plot(bins, y, 'k--', linewidth=1.5, label='Theoretical')

# Overlay a reversed cumulative histogram.
ax.hist(x, bins=bins, histtype='step', cumulative=-1,
        label='Reversed emp.')

# tidy up the figure
ax.grid(True)
ax.legend(loc='right')
ax.set_title('Cumulative step histograms')
ax.set_xlabel('Annual rainfall (mm)')
ax.set_ylabel('Likelihood of occurrence')

plt.show()


dir(mlab)

['GaussianKDE',
 'Number',
 '__builtins__',
 '__cached__',
 '__doc__',
 '__file__',
 '__loader__',
 '__name__',
 '__package__',
 '__spec__',
 '_single_spectrum_docs',
 '_single_spectrum_helper',
 '_spectral_helper',
 'angle_spectrum',
 'apply_window',
 'cbook',
 'cohere',
 'complex_spectrum',
 'csd',
 'detrend',
 'detrend_linear',
 'detrend_mean',
 'detrend_none',
 'docstring',
 'functools',
 'magnitude_spectrum',
 'np',
 'phase_spectrum',
 'psd',
 'specgram',
 'stride_repeat',
 'stride_windows',
 'window_hanning',
 'window_none']


import random
import numpy as np
import matplotlib.pyplot as plt

# fake data
fs = 10  # fontsize
pos = [1, 2, 4, 5, 7, 8]
data = [np.random.normal(0, std, size=100) for std in pos]

fig, axes = plt.subplots(nrows=2, ncols=3, figsize=(6, 6))

axes[0, 0].violinplot(data, pos, points=20, widths=0.3,
                      showmeans=True, showextrema=True, showmedians=True)
axes[0, 0].set_title('Custom violinplot 1', fontsize=fs)

axes[0, 1].violinplot(data, pos, points=40, widths=0.5,
                      showmeans=True, showextrema=True, showmedians=True,
                      bw_method='silverman')
axes[0, 1].set_title('Custom violinplot 2', fontsize=fs)

axes[0, 2].violinplot(data, pos, points=60, widths=0.7, showmeans=True,
                      showextrema=True, showmedians=True, bw_method=0.5)
axes[0, 2].set_title('Custom violinplot 3', fontsize=fs)

axes[1, 0].violinplot(data, pos, points=80, vert=False, widths=0.7,
                      showmeans=True, showextrema=True, showmedians=True)
axes[1, 0].set_title('Custom violinplot 4', fontsize=fs)

axes[1, 1].violinplot(data, pos, points=100, vert=False, widths=0.9,
                      showmeans=True, showextrema=True, showmedians=True,
                      bw_method='silverman')
axes[1, 1].set_title('Custom violinplot 5', fontsize=fs)

axes[1, 2].violinplot(data, pos, points=200, vert=False, widths=1.1,
                      showmeans=True, showextrema=True, showmedians=True,
                      bw_method=0.5)
axes[1, 2].set_title('Custom violinplot 6', fontsize=fs)

for ax in axes.flatten():
    ax.set_yticklabels([])

fig.suptitle("Violin Plotting Examples")
fig.subplots_adjust(hspace=0.4)
plt.show()

	country	continent	year	lifeExp	pop	gdpPercap	iso_alpha	iso_num
11	Afghanistan	Asia	2007	43.828	31889923	974.580338	AFG	4
23	Albania	Europe	2007	76.423	3600523	5937.029526	ALB	8
35	Algeria	Africa	2007	72.301	33333216	6223.367465	DZA	12
47	Angola	Africa	2007	42.731	12420476	4797.231267	AGO	24
59	Argentina	Americas	2007	75.320	40301927	12779.379640	ARG	32

Some "Statistical Visualizations" for your projects¶

Task 1: Basic Statistics¶

Task 2: Statistical Visualization with Seaborn¶

Task 3: Statistical Visualization with Plotly¶

Task 4: Statistical Visualization with Matplotlib¶